MinT - Best Known (111, 111+37, s)-Nets in Base 4

Best Known (111, 111+37, s)-Nets in Base 4

(111, 111+37, 1028)-Net over F₄ — Constructive and digital

Digital (111, 148, 1028)-net over F₄, using

trace code for nets [i] based on digital (0, 37, 257)-net over F₂₅₆, using
- net from sequence [i] based on digital (0, 256)-sequence over F₂₅₆, using
  - generalized Faure sequence [i]
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅₆ with g(F) = 0 and N(F) ≥ 257, using
    - the rational function field F₂₅₆(x) [i]
  - Niederreiter sequence [i]

(111, 111+37, 1439)-Net over F₄ — Digital

Digital (111, 148, 1439)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(111, 111+37, 207874)-Net in Base 4 — Upper bound on s

There is no (111, 148, 207875)-net in base 4, because

1 times m-reduction [i] would yield (111, 147, 207875)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 31829 332775 536899 961455 782728 728258 169030 893080 993904 918051 129297 254128 982651 217688 058176 > 4¹⁴⁷ [i]